The design of many types of optimum digital signal processing schemes involves an assumed knowledge of various types of covariance matrices. If these matrix quantities are unknown a priori they must be estimated. In addition, many processor design criteria require a knowledge of inverse covariance matrices for the purpose of implementing various digital noise 'whitening' operations. Generally, the method for obtaining an estimated inverse covariance matrix is to estimate the original matrix and then invert it digitally. If the dimensionality of the covariance matrix doesn't preclude a digital inversion, then, in many environments, the time consumed by the inversion process does. This memorandum derives an algorithm for directly estimating the inverse of a covariance matrix. The estimation technique used is that of multidimensional gradient search. The method is applicable in a nonstationary noise environment with the inverse of an arbitrary positive definite matrix required as an initial condition.